Rocket Equation Calculator
A rocket stage with I_sp = 350 s and a mass ratio of 10 gains 7903.23 m/s of delta-v, about the speed of low Earth orbit.
7903.22613577352 m/s
Full answer, then cut to fewer decimals (not rounded):
- 7903.22613577352 m/s
- 7903.2261357735 m/s
- 7903.226135773 m/s
- 7903.22613577 m/s
- 7903.2261357 m/s
- 7903.226135 m/s
- 7903.22613 m/s
- 7903.2261 m/s
- 7903.226 m/s
- 7903.22 m/s
- 7903.2 m/s
- In km/s
- 7.903226136 km/s
- Effective exhaust velocity Isp g₀
- 3432.3275 m/s
- Mass ratio m₀/m_f
- 10
- Propellant mass fraction
- 90 %
- Propellant mass
- 90000 kg
Step-by-step solution
- Δv = I_sp × g₀ × ln(m₀ ÷ m_f)
- Δv = 350 × g₀ × ln(100000 ÷ 10000)
- Δv = 7903.226136 m/s
Rocket Equation Formula
Δv = I_sp g₀ ln(m₀ / m_f)
m₀ initial (wet) mass, m_f final (dry) mass, g₀ = 9.80665 m/s², vₑ = I_sp g₀
Worked Example
A stage with I_sp = 350 s burning from 100 t to 10 t:
- Δv = I_sp × g₀ × ln(m₀ ÷ m_f)
- Δv = 350 × g₀ × ln(100000 ÷ 10000)
- Δv = 7903.226136 m/s
Effective exhaust velocity Isp g₀: 3432.3275 m/s · Mass ratio m₀/m_f: 10 · Propellant mass fraction: 90 % · Propellant mass: 90000 kg
GATE tip
For multistage rockets add the Δv of each stage, computing each stage’s m₀ including all the stages above it as payload.
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Example: A stage with U = 300 m/s turning the whirl from 100 to 200 m/s at 288 K inlet and 88 % efficiency: Stage pressure ratio = 1.35711.
Frequently asked questions
Why do rockets have stages?
Dropping empty tanks and engines raises the mass ratio of later stages. Two stages with ratio 5 each give Δv = vₑ ln 25, more than one stage of ratio 10 with dead weight.
How much Δv reaches orbit?
About 9.3–9.5 km/s from the ground: 7.8 km/s orbital speed plus gravity and drag losses.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Rocket Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/rocket-equation-calculator/
IEEE
Scientific Converters, "Rocket Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/rocket-equation-calculator/